Can Someone Help Me With Formulas And Key Points , Urgent And Easy Please ?

Formulas And Key Points For The Following :

(1) Simplifying And Expressing Single Fraction

(2) Simplify, expressing your answer in its lowest form

(3) Complex fraction

(4) Simultaneous Equations By Substitution Method

(5) Factorizing Using Grouping

1 Answer

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  • J. J..
    Lv 7
    8 years ago
    Favorite Answer

    The easiest way to explain is to give examples. Unfortunately I do not have too much time available so I shall only do 4) Substitution method simultaneous equations now.

    2x + 4y = 22

    6x + 3y = 39

    (NB If you have an example where x or y do not have coefficients in either of the equations then use that, as it will save work)

    Step 1

    Isolate one of the variables on one side of the equals sign in either one of the equations.

    Here I shall take the top equation and isolate "x"

    2x+ 4y = 22

    Subtract 4y from both sides

    2x = 22 - 4y

    divide both sides by 2

    x = 11 - 2y

    Therefore now we have an identity for "x"

    STEP 2

    Use this by SUBSTITUTING (11 -2y) for "x" in the bottom equation

    This now becomes

    6(11 -2y) + 3y = 39

    Expand the bracket

    66 - 12y + 3y = 39

    simplify

    66 - 9y = 39

    Add 9y and subtract 39 from each side

    27 = 9y

    Divide both sides by 9

    27/9 = y

    3 = y

    STEP 3

    Now SUBSTITUTE "3" for "y" in the equation x = 11 - 2y

    x = 11 - 2*3

    x = 11 - 6

    x = 5

    Therefore the solution is x = 5, y = 3 which can also be written as

    Solution (5,3)

    STEP 4

    Now check the answer to ensure that we have not made any errors

    2x + 4y = 22

    2*5 + 4*3 = 22

    10 + 12 = 22 = Correct

    and

    6x + 3y = 39

    6*5 + 3*3 = 39

    30 + 9 =39 = Correct

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